How to make ivy's leaves colored randomly?
I will post several possible ways to achieve this kind of task. 

First way

Basically, the most intuitive way is to use separating every single leaf into new object by using P > By Loose Parts and it's already described here (also some tutorials about modeling and rendering ivy use this technique as well). 

The main downside for this is that it needs large amount of computations and may freeze PC for some time. More than that, after the procedure is finished, the 3D Viewport still will response much slower because there will be way more objects in the scene to take into account (in case of one not very large ivy  ~5000 objects, i.e. leaves). 

Second way

Some great solutions are provided in this thread. There are several of them (at least 3 different ones):


using Random group connected to Color Group;
using UV Align\Distribute addon (thus creating UV Map) and a script executing
and the third one already listed here above


The main reason why I decided to go further is that I wanted to get possibility to setup this color randomness really fast so to test some ivys while modeling environment scene (and also I didn't find that thread from the beginning).

Third way

This way assumes using 2 UV maps, one for different leaves' color, while another - for actually the texture (image based). Basically it is one of those listed in the BA thread (except for the script), only combined with another solutions.

After the ivy is created, it has UV map by default, and it's for actually image texture as is told above. 
Therefore create one more UV map (I called it "Leaves-1"), it willl serve for different leaves' color task. With this map selected and set to active, enter Edit mode, U > Lightmap Pack (you may also use Smart UV Project option as well, it will fit ivy leaves' needs).  After this is done, with leaves still selected, in Object Data tab, UV maps scroll hit that small camera button next to the default map so it to be one used for rendering.

Now, setting nodes part. 
Basically, the nodes will be the same as they are in case of leaves / plants creating - with alpha mask using, along bump and normal maps etc. except for one thing. Instead of using Object Info node (with Random output used) what should be done if using  first way, UV Map node will be used with newly created UV map name assigned:



ColorRamp used here will determine difference between leaves' image texture color. The result on the left is with bottom ColorRamp used. The result on the right is an attempt to add several hues, so I added Mapping and Separate XYZ nodes and added one more color stop in the ColorRamp:



It is possible to change ColorRamp interpolation mode to Constant, the difference of the leaves' color will be somewhat sharper. Also some colors will become more visible (brownish in my case)


Advantages


There shouldn't be done no additional computations
Only one extra step required - this may be set up very fast
The color manipulation is rather easy and comfortable (with ColorRamp)
The result is looking somewhat convincing


Disadvantages


Some sharp color transition within one leaf sometimes may happen, especially with Interpolation mode set to Constant in ColorRamp
It's not the best solution if adding more colors to color stops is needed, it may not handle them all correctly
Because of combining color and image texture is done with MixRGB node image texture may become less visible (if the color appearence is set to high)




Addition

And with mixing one of solutions from the Second way with this one the result may look like this:



This can be achieved by connecting Random group (instead of UV Map node) to the ColorRamp from the 3rd solution. Random Group is proposed in that BA thread: